On the stressing of polygonal tubes with particular reference to the torsion of tapered tubes of trapezoidal section

Abstract

A general method for stressing polygonal tubes is described and applied to the torsion of parallel and tapered tubes of rectangular and trapezoidal section. It is assumed that the shape of the tube is maintained by a limited number of frames. In treating parallel tubes deformation of these frames in their own planes is taken into account; the effect Of this deformation is shown to be small, and in treating tapered tubes the frames are assumed to be rigid in their own planes. The method of stressing tapered tubes in torsion is applicable to any tube of trapezoidal section with one plane of symmetry, no matter how the dimensions may vary along the length of the tube; in particular the method is directly applicable to tubes having portions of their walls cut away. The successive stages in the computation are set out in tabular form and illustrated by worked examples, including cases with 'cut-outs'. The final stage in the computation involves the solution of a set of simultaneous equations equal in number to the number of frames, but these equations are of a special type, readily soluble by a straightforward process without danger of any serious loss of accuracy. The length of the computation is directly proportional to the number of frames, but it is demonstrated by examples that the stress distribution is affected only slightly by the addition of extra frames, so that in practice it should normally be permissible to ignore all but a few of the frames. In the special case of a conically tapered tube in which the wall thicknesses are uniform along the length of the tube, the results can be generalized to include the case of a tube with an infinite number of rigid frames. In this case the results obtained by the present method become identical with those obtained by Williams in R. & M. 1761 and by others using Williams's method. The author wishes gratefully to acknowledge the help he has received in the preparation of this paper from Messrs. H. E. Smith and A. E. Johnson of the National Physical Laboratory, Mr. W. S. Hemp of the Bristol Aeroplane Co., Ltd., and Mr.E.H. Atkin of Messrs. A. V. Roeand Co., Ltd.